Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C

Percentage Accurate: 58.5% → 98.4%

Time: 16.8s

Alternatives: 13

Speedup: 4.4×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

Initial Program: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{\frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x} - 4.5380502827815}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      INFINITY)
   (/
    (*
     (fma x x -4.0)
     (/
      (fma
       x
       (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
       z)
      (fma
       x
       (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
       47.066876606)))
    (+ x 2.0))
   (/
    (+ x -2.0)
    (+
     0.24013125253755718
     (/
      (-
       (/
        (-
         77.83123209621681
         (/ (fma y 0.05766301844525606 1321.0120716024157) x))
        x)
       4.5380502827815)
      x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= ((double) INFINITY)) {
		tmp = (fma(x, x, -4.0) * (fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606))) / (x + 2.0);
	} else {
		tmp = (x + -2.0) / (0.24013125253755718 + ((((77.83123209621681 - (fma(y, 0.05766301844525606, 1321.0120716024157) / x)) / x) - 4.5380502827815) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= Inf)
		tmp = Float64(Float64(fma(x, x, -4.0) * Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606))) / Float64(x + 2.0));
	else
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(Float64(Float64(Float64(77.83123209621681 - Float64(fma(y, 0.05766301844525606, 1321.0120716024157) / x)) / x) - 4.5380502827815) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x * x + -4.0), $MachinePrecision] * N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(N[(N[(N[(77.83123209621681 - N[(N[(y * 0.05766301844525606 + 1321.0120716024157), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 4.5380502827815), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < +inf.0

   1. Initial program 93.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}}{x + 2}} \]

   if +inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{{x}^{3}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]
   6. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      2. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{{x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot {x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      4. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      5. lower-*.f64 0.0

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   7. Simplified 0.0%

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   8. Taylor expanded in x around -inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} + -1 \cdot \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x + -2}{\frac{25000000000}{104109730557} + \color{blue}{\left(\mathsf{neg}\left(\frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}\right)\right)}} \]

      2. unsub-neg N/A

         \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} - \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} - \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{25000000000}{104109730557} - \color{blue}{\frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

   10. Simplified 99.7%

       \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 - \frac{4.5380502827815 - \frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x}}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}}{x + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{\frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x} - 4.5380502827815}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{\frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x} - 4.5380502827815}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      INFINITY)
   (*
    (/
     (fma
      x
      (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
      z)
     (fma
      x
      (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
      47.066876606))
    (+ x -2.0))
   (/
    (+ x -2.0)
    (+
     0.24013125253755718
     (/
      (-
       (/
        (-
         77.83123209621681
         (/ (fma y 0.05766301844525606 1321.0120716024157) x))
        x)
       4.5380502827815)
      x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= ((double) INFINITY)) {
		tmp = (fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)) * (x + -2.0);
	} else {
		tmp = (x + -2.0) / (0.24013125253755718 + ((((77.83123209621681 - (fma(y, 0.05766301844525606, 1321.0120716024157) / x)) / x) - 4.5380502827815) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= Inf)
		tmp = Float64(Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606)) * Float64(x + -2.0));
	else
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(Float64(Float64(Float64(77.83123209621681 - Float64(fma(y, 0.05766301844525606, 1321.0120716024157) / x)) / x) - 4.5380502827815) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(N[(N[(N[(77.83123209621681 - N[(N[(y * 0.05766301844525606 + 1321.0120716024157), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 4.5380502827815), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < +inf.0

   1. Initial program 93.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(x + -2\right)} \]

   if +inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{{x}^{3}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]
   6. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      2. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{{x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot {x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      4. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      5. lower-*.f64 0.0

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   7. Simplified 0.0%

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   8. Taylor expanded in x around -inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} + -1 \cdot \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x + -2}{\frac{25000000000}{104109730557} + \color{blue}{\left(\mathsf{neg}\left(\frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}\right)\right)}} \]

      2. unsub-neg N/A

         \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} - \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} - \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{25000000000}{104109730557} - \color{blue}{\frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

   10. Simplified 99.7%

       \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 - \frac{4.5380502827815 - \frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x}}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)} \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{\frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x} - 4.5380502827815}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x \cdot x, x \cdot x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{\frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x} - 4.5380502827815}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      INFINITY)
   (*
    (fma
     x
     (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
     z)
    (/ (+ x -2.0) (fma (* x x) (* x x) 47.066876606)))
   (/
    (+ x -2.0)
    (+
     0.24013125253755718
     (/
      (-
       (/
        (-
         77.83123209621681
         (/ (fma y 0.05766301844525606 1321.0120716024157) x))
        x)
       4.5380502827815)
      x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= ((double) INFINITY)) {
		tmp = fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) * ((x + -2.0) / fma((x * x), (x * x), 47.066876606));
	} else {
		tmp = (x + -2.0) / (0.24013125253755718 + ((((77.83123209621681 - (fma(y, 0.05766301844525606, 1321.0120716024157) / x)) / x) - 4.5380502827815) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= Inf)
		tmp = Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) * Float64(Float64(x + -2.0) / fma(Float64(x * x), Float64(x * x), 47.066876606)));
	else
		tmp = Float64(Float64(x + -2.0) / Float64(0.24013125253755718 + Float64(Float64(Float64(Float64(77.83123209621681 - Float64(fma(y, 0.05766301844525606, 1321.0120716024157) / x)) / x) - 4.5380502827815) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x + -2.0), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / N[(0.24013125253755718 + N[(N[(N[(N[(77.83123209621681 - N[(N[(y * 0.05766301844525606 + 1321.0120716024157), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 4.5380502827815), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < +inf.0

   1. Initial program 93.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{{x}^{3}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]
   6. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      2. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{{x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot {x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      4. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      5. lower-*.f64 96.6

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   7. Simplified 96.6%

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{x + -2}}{\frac{x \cdot \left(x \cdot \left(x \cdot x\right)\right) + \frac{23533438303}{500000000}}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{x \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) + \frac{23533438303}{500000000}}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{x \cdot \color{blue}{\left(x \cdot \left(x \cdot x\right)\right)} + \frac{23533438303}{500000000}}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      4. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\color{blue}{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      5. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}{x \cdot \left(x \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right)} + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      6. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}{x \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right)} + y\right) + z}} \]

      7. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}{x \cdot \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right)} + z}} \]

      8. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}{\color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}}} \]

      9. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{x + -2}{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)} \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)} \]

      10. *-commutative N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}} \]

   9. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x \cdot x, x \cdot x, 47.066876606\right)}} \]

   if +inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{{x}^{3}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]
   6. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      2. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{{x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot {x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      4. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      5. lower-*.f64 0.0

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   7. Simplified 0.0%

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   8. Taylor expanded in x around -inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} + -1 \cdot \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x + -2}{\frac{25000000000}{104109730557} + \color{blue}{\left(\mathsf{neg}\left(\frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}\right)\right)}} \]

      2. unsub-neg N/A

         \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} - \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557} - \frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{25000000000}{104109730557} - \color{blue}{\frac{\frac{49187182759625000000000}{10838835996651139530249} + -1 \cdot \frac{\frac{87826964544759006581385625000000000}{1128428295162862690821234941118693} + -1 \cdot \frac{\frac{155192981348266099328266580997221515625000000000}{117480365762300501174186766773860888386002001} - \frac{-625000000000000000000}{10838835996651139530249} \cdot y}{x}}{x}}{x}}} \]

   10. Simplified 99.7%

       \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718 - \frac{4.5380502827815 - \frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x}}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x \cdot x, x \cdot x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{\frac{77.83123209621681 - \frac{\mathsf{fma}\left(y, 0.05766301844525606, 1321.0120716024157\right)}{x}}{x} - 4.5380502827815}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x \cdot x, x \cdot x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      INFINITY)
   (*
    (fma
     x
     (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
     z)
    (/ (+ x -2.0) (fma (* x x) (* x x) 47.066876606)))
   (/ (+ x -2.0) 0.24013125253755718)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= ((double) INFINITY)) {
		tmp = fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) * ((x + -2.0) / fma((x * x), (x * x), 47.066876606));
	} else {
		tmp = (x + -2.0) / 0.24013125253755718;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= Inf)
		tmp = Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) * Float64(Float64(x + -2.0) / fma(Float64(x * x), Float64(x * x), 47.066876606)));
	else
		tmp = Float64(Float64(x + -2.0) / 0.24013125253755718);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x + -2.0), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < +inf.0

   1. Initial program 93.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{{x}^{3}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]
   6. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      2. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{{x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot {x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      4. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      5. lower-*.f64 96.6

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   7. Simplified 96.6%

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{x + -2}}{\frac{x \cdot \left(x \cdot \left(x \cdot x\right)\right) + \frac{23533438303}{500000000}}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{x \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) + \frac{23533438303}{500000000}}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{x \cdot \color{blue}{\left(x \cdot \left(x \cdot x\right)\right)} + \frac{23533438303}{500000000}}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      4. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\color{blue}{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}}{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      5. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}{x \cdot \left(x \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right)} + \frac{4297481763}{31250000}\right) + y\right) + z}} \]

      6. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}{x \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right)} + y\right) + z}} \]

      7. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}{x \cdot \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right)} + z}} \]

      8. lift-fma.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}{\color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}}} \]

      9. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{x + -2}{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)} \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)} \]

      10. *-commutative N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x, x \cdot \left(x \cdot x\right), \frac{23533438303}{500000000}\right)}} \]

   9. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x \cdot x, x \cdot x, 47.066876606\right)}} \]

   if +inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557}}} \]
   6. Step-by-step derivation

   7. Simplified 99.5%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right) \cdot \frac{x + -2}{\mathsf{fma}\left(x \cdot x, x \cdot x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+36}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, 137.519416416, y\right), z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -4.8e+26)
     t_0
     (if (<= x 1.7e+36)
       (/
        (* (- x 2.0) (fma x (fma x 137.519416416 y) z))
        (+
         (*
          x
          (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -4.8e+26) {
		tmp = t_0;
	} else if (x <= 1.7e+36) {
		tmp = ((x - 2.0) * fma(x, fma(x, 137.519416416, y), z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -4.8e+26)
		tmp = t_0;
	elseif (x <= 1.7e+36)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(x, fma(x, 137.519416416, y), z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -4.8e+26], t$95$0, If[LessEqual[x, 1.7e+36], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(x * N[(x * 137.519416416 + y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.80000000000000009e26 or 1.6999999999999999e36 < x

   1. Initial program 8.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 12.4%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557}}} \]
   6. Step-by-step derivation

   7. Simplified 94.4%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -4.80000000000000009e26 < x < 1.6999999999999999e36

   1. Initial program 97.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(z + x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right)\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right) + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. lower-fma.f64 N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(x, y + \frac{4297481763}{31250000} \cdot x, z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \color{blue}{\frac{4297481763}{31250000} \cdot x + y}, z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \color{blue}{x \cdot \frac{4297481763}{31250000}} + y, z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      5. lower-fma.f64 97.3

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, 137.519416416, y\right)}, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Simplified 97.3%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, 137.519416416, y\right), z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+36}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, 137.519416416, y\right), z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -1.6e+18)
     t_0
     (if (<= x 3.5e+35)
       (/
        (+ x -2.0)
        (/
         47.066876606
         (fma
          x
          (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
          z)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1.6e+18) {
		tmp = t_0;
	} else if (x <= 3.5e+35) {
		tmp = (x + -2.0) / (47.066876606 / fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -1.6e+18)
		tmp = t_0;
	elseif (x <= 3.5e+35)
		tmp = Float64(Float64(x + -2.0) / Float64(47.066876606 / fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -1.6e+18], t$95$0, If[LessEqual[x, 3.5e+35], N[(N[(x + -2.0), $MachinePrecision] / N[(47.066876606 / N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e18 or 3.5000000000000001e35 < x

   1. Initial program 8.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 12.4%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557}}} \]
   6. Step-by-step derivation

   7. Simplified 94.4%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -1.6e18 < x < 3.5000000000000001e35

   1. Initial program 97.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{x + -2}{\frac{\color{blue}{\frac{23533438303}{500000000}}}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]
   6. Step-by-step derivation

   7. Simplified 92.9%

      \[\leadsto \frac{x + -2}{\frac{\color{blue}{47.066876606}}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 90.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, -0.4223685497810532, \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right), \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.0212463641547976\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -1.6e+18)
     t_0
     (if (<= x 3.5e+35)
       (fma
        -0.0424927283095952
        z
        (*
         x
         (fma
          x
          (fma
           x
           -0.4223685497810532
           (fma 0.0212463641547976 y -5.843575199059173))
          (fma -0.0424927283095952 y (* z 0.0212463641547976)))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1.6e+18) {
		tmp = t_0;
	} else if (x <= 3.5e+35) {
		tmp = fma(-0.0424927283095952, z, (x * fma(x, fma(x, -0.4223685497810532, fma(0.0212463641547976, y, -5.843575199059173)), fma(-0.0424927283095952, y, (z * 0.0212463641547976)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -1.6e+18)
		tmp = t_0;
	elseif (x <= 3.5e+35)
		tmp = fma(-0.0424927283095952, z, Float64(x * fma(x, fma(x, -0.4223685497810532, fma(0.0212463641547976, y, -5.843575199059173)), fma(-0.0424927283095952, y, Float64(z * 0.0212463641547976)))));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -1.6e+18], t$95$0, If[LessEqual[x, 3.5e+35], N[(-0.0424927283095952 * z + N[(x * N[(x * N[(x * -0.4223685497810532 + N[(0.0212463641547976 * y + -5.843575199059173), $MachinePrecision]), $MachinePrecision] + N[(-0.0424927283095952 * y + N[(z * 0.0212463641547976), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e18 or 3.5000000000000001e35 < x

   1. Initial program 8.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 12.4%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557}}} \]
   6. Step-by-step derivation

   7. Simplified 94.4%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -1.6e18 < x < 3.5000000000000001e35

   1. Initial program 97.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{{x}^{3}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]
   6. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      2. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{{x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot {x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      4. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      5. lower-*.f64 97.1

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   7. Simplified 97.1%

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{-49698921037}{117667191515} \cdot x + \frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right)} \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{-49698921037}{117667191515} \cdot x + \frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, \color{blue}{x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + x \cdot \left(\frac{-49698921037}{117667191515} \cdot x + \frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \color{blue}{\left(x \cdot \left(\frac{-49698921037}{117667191515} \cdot x + \frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right)\right) + \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \color{blue}{\mathsf{fma}\left(x, \frac{-49698921037}{117667191515} \cdot x + \frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right), \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \color{blue}{x \cdot \frac{-49698921037}{117667191515}} + \frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right), \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right)\right)}, \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \frac{500000000}{23533438303} \cdot \color{blue}{\left(y + \left(\mathsf{neg}\left(\frac{4297481763}{15625000}\right)\right)\right)}\right), \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)\right) \]

      8. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \color{blue}{\frac{500000000}{23533438303} \cdot y + \frac{500000000}{23533438303} \cdot \left(\mathsf{neg}\left(\frac{4297481763}{15625000}\right)\right)}\right), \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \frac{500000000}{23533438303} \cdot y + \frac{500000000}{23533438303} \cdot \color{blue}{\frac{-4297481763}{15625000}}\right), \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \frac{500000000}{23533438303} \cdot y + \color{blue}{\frac{-137519416416}{23533438303}}\right), \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \color{blue}{\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-137519416416}{23533438303}\right)}\right), \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-137519416416}{23533438303}\right)\right), \frac{500000000}{23533438303} \cdot \color{blue}{\left(-2 \cdot y + z\right)}\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-137519416416}{23533438303}\right)\right), \color{blue}{\frac{500000000}{23533438303} \cdot \left(-2 \cdot y\right) + \frac{500000000}{23533438303} \cdot z}\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-137519416416}{23533438303}\right)\right), \color{blue}{\left(\frac{500000000}{23533438303} \cdot -2\right) \cdot y} + \frac{500000000}{23533438303} \cdot z\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-137519416416}{23533438303}\right)\right), \color{blue}{\frac{-1000000000}{23533438303}} \cdot y + \frac{500000000}{23533438303} \cdot z\right)\right) \]

      16. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-137519416416}{23533438303}\right)\right), \color{blue}{\mathsf{fma}\left(\frac{-1000000000}{23533438303}, y, \frac{500000000}{23533438303} \cdot z\right)}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1000000000}{23533438303}, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{-49698921037}{117667191515}, \mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-137519416416}{23533438303}\right)\right), \mathsf{fma}\left(\frac{-1000000000}{23533438303}, y, \color{blue}{z \cdot \frac{500000000}{23533438303}}\right)\right)\right) \]

      18. lower-*.f64 92.9

          \[\leadsto \mathsf{fma}\left(-0.0424927283095952, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, -0.4223685497810532, \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right), \mathsf{fma}\left(-0.0424927283095952, y, \color{blue}{z \cdot 0.0212463641547976}\right)\right)\right) \]

   10. Simplified 92.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-0.0424927283095952, z, x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, -0.4223685497810532, \mathsf{fma}\left(0.0212463641547976, y, -5.843575199059173\right)\right), \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.0212463641547976\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 90.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot 0.0212463641547976, \mathsf{fma}\left(x, y + -275.038832832, \mathsf{fma}\left(-2, y, z\right)\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -1.6e+18)
     t_0
     (if (<= x 3.5e+35)
       (fma
        (* x 0.0212463641547976)
        (fma x (+ y -275.038832832) (fma -2.0 y z))
        (* z -0.0424927283095952))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1.6e+18) {
		tmp = t_0;
	} else if (x <= 3.5e+35) {
		tmp = fma((x * 0.0212463641547976), fma(x, (y + -275.038832832), fma(-2.0, y, z)), (z * -0.0424927283095952));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -1.6e+18)
		tmp = t_0;
	elseif (x <= 3.5e+35)
		tmp = fma(Float64(x * 0.0212463641547976), fma(x, Float64(y + -275.038832832), fma(-2.0, y, z)), Float64(z * -0.0424927283095952));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -1.6e+18], t$95$0, If[LessEqual[x, 3.5e+35], N[(N[(x * 0.0212463641547976), $MachinePrecision] * N[(x * N[(y + -275.038832832), $MachinePrecision] + N[(-2.0 * y + z), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e18 or 3.5000000000000001e35 < x

   1. Initial program 8.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 12.4%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557}}} \]
   6. Step-by-step derivation

   7. Simplified 94.4%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -1.6e18 < x < 3.5000000000000001e35

   1. Initial program 97.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{{x}^{3}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]
   6. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      2. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{{x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot {x}^{2}}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      4. unpow2 N/A

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, \frac{23533438303}{500000000}\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), y\right), z\right)}} \]

      5. lower-*.f64 97.1

         \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, x \cdot \color{blue}{\left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   7. Simplified 97.1%

      \[\leadsto \frac{x + -2}{\frac{\mathsf{fma}\left(x, \color{blue}{x \cdot \left(x \cdot x\right)}, 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(x \cdot \left(y - \frac{4297481763}{15625000}\right)\right) + \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x \cdot \left(\frac{500000000}{23533438303} \cdot \left(x \cdot \left(y - \frac{4297481763}{15625000}\right)\right) + \frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right)\right) + \frac{-1000000000}{23533438303} \cdot z} \]

      2. distribute-lft-out N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{500000000}{23533438303} \cdot \left(x \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(z + -2 \cdot y\right)\right)\right)} + \frac{-1000000000}{23533438303} \cdot z \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(x \cdot \frac{500000000}{23533438303}\right) \cdot \left(x \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(z + -2 \cdot y\right)\right)} + \frac{-1000000000}{23533438303} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{500000000}{23533438303} \cdot x\right)} \cdot \left(x \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(z + -2 \cdot y\right)\right) + \frac{-1000000000}{23533438303} \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{500000000}{23533438303} \cdot x, x \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(z + -2 \cdot y\right), \frac{-1000000000}{23533438303} \cdot z\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{500000000}{23533438303} \cdot x}, x \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(z + -2 \cdot y\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot x, \color{blue}{\mathsf{fma}\left(x, y - \frac{4297481763}{15625000}, z + -2 \cdot y\right)}, \frac{-1000000000}{23533438303} \cdot z\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot x, \mathsf{fma}\left(x, \color{blue}{y + \left(\mathsf{neg}\left(\frac{4297481763}{15625000}\right)\right)}, z + -2 \cdot y\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      9. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot x, \mathsf{fma}\left(x, \color{blue}{y + \left(\mathsf{neg}\left(\frac{4297481763}{15625000}\right)\right)}, z + -2 \cdot y\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot x, \mathsf{fma}\left(x, y + \color{blue}{\frac{-4297481763}{15625000}}, z + -2 \cdot y\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot x, \mathsf{fma}\left(x, y + \frac{-4297481763}{15625000}, \color{blue}{-2 \cdot y + z}\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot x, \mathsf{fma}\left(x, y + \frac{-4297481763}{15625000}, \color{blue}{\mathsf{fma}\left(-2, y, z\right)}\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      13. lower-*.f64 92.8

          \[\leadsto \mathsf{fma}\left(0.0212463641547976 \cdot x, \mathsf{fma}\left(x, y + -275.038832832, \mathsf{fma}\left(-2, y, z\right)\right), \color{blue}{-0.0424927283095952 \cdot z}\right) \]

   10. Simplified 92.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(0.0212463641547976 \cdot x, \mathsf{fma}\left(x, y + -275.038832832, \mathsf{fma}\left(-2, y, z\right)\right), -0.0424927283095952 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot 0.0212463641547976, \mathsf{fma}\left(x, y + -275.038832832, \mathsf{fma}\left(-2, y, z\right)\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.1:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -1.6e+18)
     t_0
     (if (<= x 2.1)
       (fma
        x
        (fma -0.0424927283095952 y (* z 0.3041881842569256))
        (* z -0.0424927283095952))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1.6e+18) {
		tmp = t_0;
	} else if (x <= 2.1) {
		tmp = fma(x, fma(-0.0424927283095952, y, (z * 0.3041881842569256)), (z * -0.0424927283095952));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -1.6e+18)
		tmp = t_0;
	elseif (x <= 2.1)
		tmp = fma(x, fma(-0.0424927283095952, y, Float64(z * 0.3041881842569256)), Float64(z * -0.0424927283095952));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -1.6e+18], t$95$0, If[LessEqual[x, 2.1], N[(x * N[(-0.0424927283095952 * y + N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e18 or 2.10000000000000009 < x

   1. Initial program 10.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 15.0%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557}}} \]
   6. Step-by-step derivation

   7. Simplified 91.0%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -1.6e18 < x < 2.10000000000000009

   1. Initial program 99.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, -4\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}}{x + 2}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x \cdot \left(\frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z\right) + \frac{-1000000000}{23533438303} \cdot z} \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{-1000000000}{23533438303} \cdot y - \frac{-168466327098500000000}{553822718361107519809} \cdot z, \frac{-1000000000}{23533438303} \cdot z\right)} \]

      3. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{-1000000000}{23533438303} \cdot y + \left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)}, \frac{-1000000000}{23533438303} \cdot z\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(\frac{-1000000000}{23533438303}, y, \mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809} \cdot z\right)\right)}, \frac{-1000000000}{23533438303} \cdot z\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(\frac{-1000000000}{23533438303}, y, \mathsf{neg}\left(\color{blue}{z \cdot \frac{-168466327098500000000}{553822718361107519809}}\right)\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(\frac{-1000000000}{23533438303}, y, \color{blue}{z \cdot \left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right)}\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(\frac{-1000000000}{23533438303}, y, \color{blue}{z \cdot \left(\mathsf{neg}\left(\frac{-168466327098500000000}{553822718361107519809}\right)\right)}\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(\frac{-1000000000}{23533438303}, y, z \cdot \color{blue}{\frac{168466327098500000000}{553822718361107519809}}\right), \frac{-1000000000}{23533438303} \cdot z\right) \]

      9. lower-*.f64 89.0

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), \color{blue}{-0.0424927283095952 \cdot z}\right) \]

   7. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), -0.0424927283095952 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2.1:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), z \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{z \cdot -2}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -1.6e+18)
     t_0
     (if (<= x 7.8e+17) (/ (* z -2.0) 47.066876606) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1.6e+18) {
		tmp = t_0;
	} else if (x <= 7.8e+17) {
		tmp = (z * -2.0) / 47.066876606;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-1.6d+18)) then
        tmp = t_0
    else if (x <= 7.8d+17) then
        tmp = (z * (-2.0d0)) / 47.066876606d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1.6e+18) {
		tmp = t_0;
	} else if (x <= 7.8e+17) {
		tmp = (z * -2.0) / 47.066876606;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -1.6e+18:
		tmp = t_0
	elif x <= 7.8e+17:
		tmp = (z * -2.0) / 47.066876606
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -1.6e+18)
		tmp = t_0;
	elseif (x <= 7.8e+17)
		tmp = Float64(Float64(z * -2.0) / 47.066876606);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -1.6e+18)
		tmp = t_0;
	elseif (x <= 7.8e+17)
		tmp = (z * -2.0) / 47.066876606;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -1.6e+18], t$95$0, If[LessEqual[x, 7.8e+17], N[(N[(z * -2.0), $MachinePrecision] / 47.066876606), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e18 or 7.8e17 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 14.4%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557}}} \]
   6. Step-by-step derivation

   7. Simplified 92.3%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -1.6e18 < x < 7.8e17

   1. Initial program 98.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{\left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right) \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right) \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), z\right) \cdot \left(x + -2\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), \frac{4297481763}{31250000}\right), z\right) \cdot \left(x + -2\right)}{\color{blue}{\frac{23533438303}{500000000}}} \]
   7. Step-by-step derivation

   8. Simplified 68.1%

      \[\leadsto \frac{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), z\right) \cdot \left(x + -2\right)}{\color{blue}{47.066876606}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-2 \cdot z}}{\frac{23533438303}{500000000}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{\color{blue}{z \cdot -2}}{\frac{23533438303}{500000000}} \]

       2. lower-*.f64 61.4

          \[\leadsto \frac{\color{blue}{z \cdot -2}}{47.066876606} \]

   11. Simplified 61.4%

       \[\leadsto \frac{\color{blue}{z \cdot -2}}{47.066876606} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 75.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718)))
   (if (<= x -1.6e+18) t_0 (if (<= x 7.8e+17) (* z -0.0424927283095952) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1.6e+18) {
		tmp = t_0;
	} else if (x <= 7.8e+17) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-2.0d0)) / 0.24013125253755718d0
    if (x <= (-1.6d+18)) then
        tmp = t_0
    else if (x <= 7.8d+17) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double tmp;
	if (x <= -1.6e+18) {
		tmp = t_0;
	} else if (x <= 7.8e+17) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + -2.0) / 0.24013125253755718
	tmp = 0
	if x <= -1.6e+18:
		tmp = t_0
	elif x <= 7.8e+17:
		tmp = z * -0.0424927283095952
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	tmp = 0.0
	if (x <= -1.6e+18)
		tmp = t_0;
	elseif (x <= 7.8e+17)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + -2.0) / 0.24013125253755718;
	tmp = 0.0;
	if (x <= -1.6e+18)
		tmp = t_0;
	elseif (x <= 7.8e+17)
		tmp = z * -0.0424927283095952;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, If[LessEqual[x, -1.6e+18], t$95$0, If[LessEqual[x, 7.8e+17], N[(z * -0.0424927283095952), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e18 or 7.8e17 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied egg-rr 14.4%

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{x + -2}{\color{blue}{\frac{25000000000}{104109730557}}} \]
   6. Step-by-step derivation

   7. Simplified 92.3%

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -1.6e18 < x < 7.8e17

   1. Initial program 98.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \frac{-1000000000}{23533438303}} \]

      2. lower-*.f64 61.2

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   5. Simplified 61.2%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 75.6% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e+18)
   (* x 4.16438922228)
   (if (<= x 7.8e+17) (* z -0.0424927283095952) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e+18) {
		tmp = x * 4.16438922228;
	} else if (x <= 7.8e+17) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.6d+18)) then
        tmp = x * 4.16438922228d0
    else if (x <= 7.8d+17) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e+18) {
		tmp = x * 4.16438922228;
	} else if (x <= 7.8e+17) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e+18:
		tmp = x * 4.16438922228
	elif x <= 7.8e+17:
		tmp = z * -0.0424927283095952
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e+18)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 7.8e+17)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e+18)
		tmp = x * 4.16438922228;
	elseif (x <= 7.8e+17)
		tmp = z * -0.0424927283095952;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e+18], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 7.8e+17], N[(z * -0.0424927283095952), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e18 or 7.8e17 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{104109730557}{25000000000}} \]

      2. lower-*.f64 91.7

         \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   5. Simplified 91.7%

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

   if -1.6e18 < x < 7.8e17

   1. Initial program 98.9%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \frac{-1000000000}{23533438303}} \]

      2. lower-*.f64 61.2

         \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]

   5. Simplified 61.2%

      \[\leadsto \color{blue}{z \cdot -0.0424927283095952} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 44.2% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ x \cdot 4.16438922228 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 4.16438922228))

C

double code(double x, double y, double z) {
	return x * 4.16438922228;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * 4.16438922228d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 4.16438922228;
}

Python

def code(x, y, z):
	return x * 4.16438922228

Julia

function code(x, y, z)
	return Float64(x * 4.16438922228)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 4.16438922228;
end

Wolfram

code[x_, y_, z_] := N[(x * 4.16438922228), $MachinePrecision]

Derivation

1. Initial program 53.1%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{x \cdot \frac{104109730557}{25000000000}} \]

   2. lower-*.f64 48.5

      \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

5. Simplified 48.5%

   \[\leadsto \color{blue}{x \cdot 4.16438922228} \]
6. Add Preprocessing

Developer Target 1: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))
   (if (< x -3.326128725870005e+62)
     t_0
     (if (< x 9.429991714554673e+55)
       (*
        (/ (- x 2.0) 1.0)
        (/
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z)
         (+
          (*
           (+
            (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x))))
            313.399215894)
           x)
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * x)))) + 313.399215894d0) * x) + 47.066876606d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811
	tmp = 0
	if x < -3.326128725870005e+62:
		tmp = t_0
	elif x < 9.429991714554673e+55:
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / Float64(Float64(Float64(Float64(Float64(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024207 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -332612872587000500000000000000000000000000000000000000000000000) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000) (if (< x 94299917145546730000000000000000000000000000000000000000) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (+ (* (+ (+ (* 263505074721/1000000000 x) (+ (* 216700011257/5000000000 (* x x)) (* x (* x x)))) 156699607947/500000000) x) 23533438303/500000000))) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000))))

  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))